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Elastic wave propagation in 3-D periodic composites: Band gaps incorporating microstructure effects

机译：3-D周期复合材料中的弹性波传播：结合了微结构效应的带隙

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摘要

A new model for determining band gaps for elastic wave propagation in three-dimensional (3-D) periodic two-phase composites is developed using a modified couple stress theory that accounts for microstructure effects. Three types of composites, each containing a different kind of inclusion - spherical, cubic, and cube with square-rod connections, are considered, with the third one representing a co-continuous composite. The plane wave expansion method and the Bloch theorem for periodic media are employed to solve the elastic wave equations in each case, which are converted to an eigenvalue problem. The band gaps are determined from solving the characteristic equation and plotting the resulting eigen-frequencies. The new non-classical model reduces to the classical elasticity-based model when microstructure effects are suppressed. To quantitatively illustrate the newly developed model, a parametric study is conducted for 3-D periodic composites with the three kinds of inclusions. The numerical results reveal that the first band gap values predicted by the current non-classical model are smaller than those predicted by the classical elasticity-based model, and the difference between the two sets of band gap values is large when the unit cell size is very small. Also, it is seen that the volume fraction and inclusion shape have significant effects on the band gap size. These indicate that large band gaps can be attained by tailoring microstructural parameters including the unit cell size, volume fraction and inclusion shape.
机译：建立了一种新的模型，用于确定在三维（3-D）周期性两相复合材料中弹性波传播的带隙，该模型使用修正的耦合应力理论解决了微观结构的影响。考虑了三种类型的复合材料，每种类型包含不同类型的夹杂物-球形，立方和方杆连接的立方，第三种类型表示共连续复合材料。分别采用平面波展开法和周期性介质的布洛赫定理（Bloch theorem）求解每种情况下的弹性波方程，并将其转换为特征值问题。通过求解特征方程并绘制所得的本征频率来确定带隙。当微结构效应被抑制时，新的非经典模型简化为基于经典弹性的模型。为了定量说明新开发的模型，对包含三种夹杂物的3-D周期复合材料进行了参数研究。数值结果表明，当前的非经典模型预测的第一带隙值小于经典的基于弹性的模型预测的值，并且当单位像元大小为时，两组带隙值之间的差异较大。很小。另外，可以看出，体积分数和夹杂物形状对带隙尺寸具有显着影响。这些表明，通过调整微结构参数（包括晶胞大小，体积分数和夹杂物形状）可以实现较大的带隙。

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